http://hal.archives-ouvertes.fr/docs/00/21/95/66/PDF/ajp-jphyscol197940C860.pdf

 
They don't mention the weighting on the SPL figure.
 
The analogy of 160dBSPL to a jet engine sort of made sense, until I read that the paper was written about a 20kHZ test tone rather than broadband sound.
 
The test results published in that paper show that a source quantified as a 20kHz sine wave at 130.5dBSPL at 0.012 meters from it's source exhibits nonlinear transmission when sampled at 2.1 meters where the level has dropped to approximately 118dBSPL.
 
 
It makes me wonder how I would compare, in real life, a discrete sine wave at, lets say 118dB? SPL to 83dBC SPL.
 
 
 
Also, the test shows that non linearity increases with distance, and since the discussion of "Room Correction" is contextual to the effects of reflections I would like to point out that the distances involved are multiplies of the dimensions of the room and as such can become rather large.
 
I don't see any mention of why the tests were performed at such high levels, I just see the reporting of the fact that this is how the test was conducted. I might infer that the use of such high source levels was merely a convenience as the dimensions of their chamber were a constraint with regard to capability of measuring at a distance.
 
They do mention "saturation" in an off hand way. Perhaps they are implying that the non linearity only occurs at or near "saturation"? The more dramatic distortion exhibited at the longer distances and lower dBSPL seems, to me, to show that "saturation" may not be a pre requisite.  
 
One thing I could not help but notice is that the introduction emphasizes that previous tests have shown that propagation of sound pressure is non linear at other, lower test frequencies.
 
Another thing I could not help but notice was the conclusion confirming that non linearity was observed and that power losses up to 99% can occur in relatively short distances.
 
Thanks for sharing the paper, I found it very interesting and it left me wondering if there are any subsequent studies that may answer some of the questions it left me with. Good stuff!
 
 

I don't see any mention of why the test were performed at such high levels, I just see the reporting of the fact that this is how the test was conducted. I might infer that the use of such high source levels was merely a convenience as the dimension of their chamber were a constraint with regard to capability of measuring at a distance.

 
They are talking about the air itself running out of "headroom" and distorting, which only happens at extraordinarily high SPL levels.

I just made a pink noise test with a 24bit/96kHz pink noise file to get some idea of how it relates to the high frequency sine wave example.
 
I placed my SPL meter at the apex of an equilateral triangle defined by two speakers and my SPL meter. The sides of the triangle were approximately 42" long. I set the playback level of the noise to 83dBC SPL.
 
Then I moved the meter in and placed it approximately 1 " from the woofer and then the tweeter.
 
95dBC SPL at 1" from a woofer and 112dBC SPL at 1" from a tweeter.
 
 

I was just trying to see how my nominal listening experience compares to some of the SPL figures shown in the graphs on the paper about the linear/non linear sound transmission.
 
It is fairly routine for me to spend the day at 83dBCSPL at my "ear spot", If I start rocking too hard I try to check and dial back down to that level, but I never much thought about what the levels were right at the speakers.
 
 

I have a sense that, as SPL goes up, your speakers will distort much quicker than the air or reflection points will. I have no proof of this, though, nor any references that come up quickly via Google. The test would be to use a THD analyzer, driving a sinewave emitter with known-low distortion over the desired range of SPL near the emitter, then measure THD at various distances both echoic and anechoic, and over a well-chosen set of frequencies and driving SPL's.
 
If you cobble that together, you could probably publish the results! Or just post them here for us to see. Or perhaps you may have more luck than I did finding something to this effect on the web. Either way, it would be interesting to know what comes out of it all!

losguy
I have a sense that, as SPL goes up, your speakers will distort much quicker than the air or reflection points will.

I have a sense that if I try to get 83dbCSPL at my listening position from my 5w desktop computer speakers there will be some serious arguments between me and the local fire service...

OTOH my 10k pa rig would struggle to be that quiet at the same distance.


We have to assume here that the speaker/amp rating is suitable for purpose and that they can produce the required levels within their linear range. The question is whether you can insert pixie dust onto the master output to correct for spot frequency cancellation or resonance at the listening position due to room geometry.

All that matters is a "flat" response at the listening position, and you can get that with pink noise, a measurement mic, an eq and RTA.

If you're struggling to hear detail because of room reflections (reverb) get a thicker carpet....

Karyn
I have a sense that if I try to get 83dbCSPL at my listening position from my 5w desktop computer speakers there will be some serious arguments between me and the local fire service...
OTOH my 10k pa rig would struggle to be that quiet at the same distance.

If you put the 10kW PA rig at your listening position I think I'd be calling your local service to save your ears - but of course I'd still leave it to you to argue with them (if they could even hear you...)
 

We have to assume here that the speaker/amp rating is suitable for purpose and that they can produce the required levels within their linear range. The question is whether you can insert pixie dust onto the master output to correct for spot frequency cancellation or resonance at the listening position due to room geometry.

All that matters is a "flat" response at the listening position, and you can get that with pink noise, a measurement mic, an eq and RTA.

That's the point - as already stated earlier, what people usually call "flat" refers just to the amplitude response (graph of amplitude vs frequency). But that's not enough to get the "magic pixie dust" (I like that BTW). Why? Because it ignores the phase response (the graph of phase, or phase delay, vs frequency). If in addition, at the listening position, the phase response is also linear (a sloped line vs linear frequency) then you will get your magic pixie dust. A typical off-the-shelf EQ like you buy today (based on bandpass filters) can never really achieve a linear phase response correction for a room.
 
[Edited for clarity]